Rojas-Medar et al. [8] introduced the concepts of a fuzzy quasilinear space and a fuzzy quasilinear operator. They give some results in linear functional analysis extended in fuzzy setting. In this work, we contribute to the theory of normed fuzzy quasilinear spaces by introducing some of their algebraic and topological properties. By an example, we show that some fuzzy normed quasilinear spaces may fail to satisfy certain topological properties of fuzzy normed linear spaces.

fuzzy sets, fuzzy-valued mappings, fuzzy normed spaces.